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Indefinite LQ optimal control with equality constraint for discrete-time uncertain systems

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Abstract

Based on uncertainty theory, this paper studies a kind of discrete-time uncertain linear quadratic (LQ) optimal control with equality constraint for the terminal state, allowing the state and control weighting matrices in the cost function to be indefinite. First, we transform the uncertain LQ optimal control problem into an equivalent deterministic optimal control problem. Then, a necessary condition for the existence of optimal linear state feedback control is presented by means of matrix minimum principle. Moreover, the well-posedness of the uncertain LQ problem is proved by applying the technique of completing squares. Finally, an example is provided to demonstrate the effectiveness of our theoretical results.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 61273009).

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Authors and Affiliations

  1. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, China

    Yuefen Chen & Yuanguo Zhu

  2. College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, China

    Yuefen Chen

Authors
  1. Yuefen Chen
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  2. Yuanguo Zhu
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Correspondence to Yuanguo Zhu.

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Chen, Y., Zhu, Y. Indefinite LQ optimal control with equality constraint for discrete-time uncertain systems. Japan J. Indust. Appl. Math. 33, 361–378 (2016). https://doi.org/10.1007/s13160-016-0217-9

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  • DOI: https://doi.org/10.1007/s13160-016-0217-9

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